Refraction and reflection

Prove mathematically that when a plane mirror is rotated an angle theta about an axis through its center, the angle of deflection of a light is equal to 2theta. How am i to show draw this out? I have already drawn my points and lined up my angles with and without the mirror rotated. I dont know what direction to take my proof now.

it depends on what you mean by the angle of deflection. Do you mean the angle of incidense + the angle of reflection. If this is the case, rotationg the mirror by an angle [tex] \theta [/tex] would increase both the angle of incidence and the angle of reflection by [tex] \theta [/tex], resulting in an angle difference of [tex] 2\theta [/tex].

If you want to prove this just draw a diagram. Then tilt your diagram by a certain angle. See what happens.